Problem: Simplify the following expression: $k = \dfrac{40y - 30x}{10y - 40z} + \dfrac{50z + 20x}{10y - 40z}$ You can assume $x,y,z \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{40y - 30x + 50z + 20x}{10y - 40z}$ $k = \dfrac{40y - 10x + 50z}{10y - 40z}$ The numerator and denominator have a common factor of $10$, so we can simplify $k = \dfrac{4y - x + 5z}{y - 4z}$